Tire comprising at least one working layer (41). The radially outermost one thereof comprises at least one undulation (412) radially on the outside of the points of the working layer (41) that are in line with the centre of the bottom face (243) of the major groove (24) closest to undulation (412). The undulation (412) of the radially outermost working layer (41) is such that, over at least 10% of the radially outer surface (ROS) of the said working layer (41), the radial distance (do) between the radially outer surface (ROS) and the tread surface (21) is at least 1 mm less than the radial distance (dc) between the radially outer surface (ROS) and the tread surface (21), which is the distance in line with the centre of the bottom face (243) of the major groove (24) closest to the said undulation (412).